1. Field of the Invention
The present invention relates to a method of measuring a rotational amount of a body with a curved surface and a direction of a rotational axis thereof; an apparatus for measuring the rotational amount thereof and the direction of the rotational axis thereof; and a method of measuring a three-dimensional posture thereof. More particularly the present invention relates to the method of measuring the rotational amount and the like of the body with a curved surface such as a golf club head, a rugby ball, a bullet of a pistol, and the like with high accuracy by specifying the three-dimensional posture thereof.
2. Description of the Related Art
Various methods and apparatuses for measuring the rotational amount and the like of spheres such as a golf ball are known.
According to a known method, light is emitted to a sphere having a reflection tape bonded to its surface or to a sphere having a region, painted in black on its surface, not reflecting light therefrom to measure the rotational amount of the sphere from a change in the amount of reflection light obtained by the rotation of the sphere. However according to this method, since the optical amount is measured, whereas the contour of the sphere and the displacement of its posture are not measured, it is impossible to specify the direction of the rotational axis and the like of the sphere. Thus normally, the rotational amount of the sphere and the direction of its rotational axis are found from a displacement situation of marks given to each of a plurality of images of a sphere photographed at predetermined intervals when the sphere having the marks on its surface is flying in rotation.
As apparatuses and methods of finding the rotational amount and the like of the sphere from images of a photographed mark-given sphere, the following measuring apparatuses and methods are known: The apparatus for measuring the rotational amount of the sphere disclosed in U.S. Pat. No. 2,810,320, the method of measuring the motion of a golf club head disclosed in Japanese Patent Application Laid-Open No. 10-186474, and the apparatus for measuring the flight characteristic of sporting goods disclosed in U.S. Pat. No. 2,950,450.
In the measuring apparatus disclosed in U.S. Pat. No. 2,810,320, as shown in FIGS. 10A and 10B, the sphere T, having the center C, to which the marks P and Q are given is photographed twice to obtain two two-dimensional images G1 and G2, and the radius of the sphere in each of the two-dimensional images G1 and G2 is specified as the unit radius. Further the three-dimensional coordinate of each of the marks P and Q and the center C is computed from the two-dimensional coordinate on the two-dimensional image G1. The three-dimensional coordinate of each of the marks P′ and Q′ and the center C′ is also computed from the two-dimensional coordinate on the two-dimensional image G2. These computed three-dimensional coordinates are set as three-dimensional vectors to find the vector movement amount between the two images G1 and G2 to thereby compute the rotational amount of the sphere T and the direction of its rotational axis.
As shown in FIGS. 11A and 11B, in the measuring method disclosed in Japanese Patent Application Laid-Open No. 10-186474, the sensor 2 that detects the motion of a club when it hits the ball B1 is used to determine a photographing timing. The ball B1 is photographed at a predetermined interval by the first and second cameras 1A and 1B. Thereby as shown in FIG. 11B, the ball image G3 having the two balls B1 and B1′ photographed thereon is obtained. The two-dimensional ball image G3 is processed by the method similar to that of the measuring apparatus disclosed in U.S. Pat. No. 2,810,320 to compute the rotational amount and the direction of its rotational axis.
With reference to FIGS. 12A and 12B, in the measuring apparatus 4 disclosed in U.S. Pat. No. 2,950,450, the balls B2 and B2′ to which the marks Ba have been given are photographed by the synchronized cameras 5A and 5B to provide one picture in which the image of each of the balls B2 and B2′ is present. The three-dimensional coordinate of the mark Ba is obtained based on a principle similar to the triangulation by relating the principle to the relationship between the visual field of the camera 5A and that of the camera 5B. Thereby as shown in FIG. 12B, a view of the three-dimensional region of the balls B2 and B2′ is obtained to measure the characteristics of the ball. The method of obtaining the three-dimensional coordinate in this manner is known as DLT (Direct Liner Transformation).
In addition to the above-described apparatuses and method, the apparatus 6 for detecting the posture of an unspherical three-dimensional object is disclosed in Japanese Patent Application Laid-Open No. 7-302341, as shown in FIG. 13. The posture detection apparatus 6 measures the posture of the three-dimensional object, based on a genetic algorithm. That is, a goodness-of-fit is found by comparing a plurality of images of the three-dimensional object 8 photographed with a plurality of cameras 7a-7n with a plurality of imaginary images of the imaginary three-dimensional object 9 formed in correspondence to the three-dimensional object 8. Based on the genetic algorithm conforming to the goodness-of-fit, the posture of the three-dimensional object 8 is detected by changing the posture of the imaginary three-dimensional object 9.
In the measuring apparatus shown in FIGS. 10A and 10B and the measuring method shown in FIGS. 11A and 11B, because the radius of the ball image is used in computations for measurement, the accuracy of the three-dimensional vector to be computed depends on the accuracy of the radii of the sphere obtained from the images. Thus it is necessary to highly accurately photograph the images on the basis of which the measurement is made and find the radius of the sphere with high accuracy from the photographed images. To obtain a still image of the ball flying at a high speed, it is necessary to use a high-speed camera having a high-speed shutter. However because the high-speed shutter opens in a very short period of time, it is difficult to obtain a sufficient amount of light.
The photographed ball image is comparatively clear in the vicinity of the center of the ball, because the center of the ball confronts the camera. On the other hand, it is difficult to clearly capture the contour of the ball. Even though the manner of emitting the ball is adjusted, it is difficult to solve this problem. Consequently the contour of the photographed image of the ball is unclear. Thus the radius of the ball is read with low accuracy from the ball image, which causes the rotational amount of the ball and the like to be measured with low accuracy.
In the measuring apparatus shown in FIGS. 12A and 12B, the three-dimensional coordinates of the marks given to the surface of the ball are obtained not by using the radius of the ball image but on the basis of the length of an actual space. Thus it is unnecessary to photograph the contour of the ball clearly and the problem of shortage of luminous intensity rarely occurs. Further measuring apparatus shown in FIGS. 12A and 12B has an advantage of reducing a burden on the measuring equipment. However to find the three-dimensional coordinates of the marks given to the surface of the ball with high accuracy, it is necessary to obtain images of the ball in a comparatively large size to allow the marks to be read accurately. To photograph the ball in a large size, it is necessary to obtain the two images of the ball by photographing it at a reduced interval, which reduces the rotational amount of one ball image with respect to that of the other ball image.
To measure the rotational amount of the ball with high accuracy, it is necessary to increase the moving distance of each mark to thereby increase the displacement of the position of the mark, i.e., increase the rotational amount of one ball image with respect to that of the other ball image, which necessitates a condition reciprocal to the increasing of the ball image.
Thus it is possible to measure the three-dimensional coordinates of the marks with high accuracy by increasing the ball image. However, because the change of the positions between both images is small, the rotational amount of the ball cannot be measured with high accuracy. In the case where the ball is photographed in such a way as to increase the rotational amount of the other ball image with respect to that of the one ball image, it is necessary to photograph the ball at a long interval. In this case, although the rotational amount of the ball can be measured with high accuracy, the ball images are small. Therefore the three-dimensional coordinates of the marks are measured with low accuracy. Thus the measuring apparatus is incapable of measuring both the three-dimensional coordinates of the marks and the rotational amount of the ball with high accuracy.
To solve the above-described problem, it is conceivable to prepare two sets of measuring apparatuses to obtain one image of the ball with a first measuring apparatus and the other image thereof with a second measuring apparatus to measure both the three-dimensional coordinate of each mark and the rotational amount of the ball with high accuracy. However in carrying out measurement, it is necessary to make a calibration by associating the operation of four cameras of both sets of the measuring apparatuses with each other. Furthermore the measuring apparatus is required to have a very complicated construction and is hence very expensive. As such, it is difficult to use two sets of the measuring apparatuses.
Further in computing the rotational amount of the ball from the movement amount of the mark given to the surface of the photographed ball, it is necessary to recognize a particular mark on the other ball image corresponding to the particular mark on the one ball image. In the case where the direction of the rotational axis of the ball can be estimated and the change of the rotational amount of the other ball image with respect to that of the one ball image is small, it is comparatively easy to recognize the particular mark on the other ball image corresponding to the particular mark on the one ball image. However in the case where the direction of the rotational axis of the ball cannot be estimated because the direction of the rotational axis of the ball changes greatly in each measurement or in the case where the change of the rotational amount of the other ball image with respect to that of the one ball image is large, it is very difficult to recognize the particular mark on the other ball image corresponding to the particular mark on the one ball image. In this case, there is a possibility that the rotational amount of the ball and the like cannot be measured by means of an automatic recognition program of a computer. In the case where a man recognizes the particular mark on the other ball image corresponding to the particular mark on the one ball image, it takes much time and may make an erroneous recognition of the mark.
In addition, it is impossible to make measurement in the case where the mark which has appeared on the one ball image rotates to the reverse side of the other ball image and does not appear on the surface thereof. In this case, there is a limitation in the measuring direction of the camera and the rotational direction of the ball. Thus the measuring apparatus has a problem of having difficulty in making measurement in an optimum situation.
In the posture detection apparatus 6 shown in FIG. 13, since a plurality of cameras 7a-7n is used, the measuring cost is high. The ball is symmetrical with respect to the axis passing through its center. Thus when the posture, namely, the direction of the ball changes, there is no change among the images of the ball photographed by the posture detection apparatus 6. That is, even though the ball images and the imaginary images are compared with each other, the posture of the ball cannot be specified. Further in the posture detection apparatus 6, the goodness-of-fit is determined on the basis of an overlapping degree of a plurality of images. Thus it is necessary to provide a clear contour of the ball image. However in the case where the posture of a body with the curved surface such as a golf club head which moves at a high speed is measured, it is difficult for the cameras 7a-7n to follow a high-speed movement of the body with the curved surface and photograph it. It is almost impossible that all images of the ball are clear. Because the goodness-of-fit is determined on the basis of images containing a considerable degree of errors, the posture detection apparatus 6 is incapable of measuring the posture of the ball with high accuracy.
The above-described conventional methods are intended to measure the rotational amount and the like of the sphere such as the golf ball, but are incapable of measuring the rotational amount and the like of a body with a curved surface such as a golf club head, a rugby ball, a bullet of a pistol, and the like.